About PR#14067, now I understand why (Date + difftime) does not use '+.Date'.
But, before I understand, it was surprising. The surprise is also reflected in
the post "Problem with +(POSIXt, difftime) dispatching -- WAS: How to create
sequence of constant time interval" in R-help 2009-02-17.

Reading the documentation above suggests me that I can use (Date + difftime),
which I expect to use date/time arithmetic. PR#13369 also mentions that.

So, the documentation should mention that, to add "Date" with "difftime",
'+.Date' should be called directly, better with example. Alternatively, the
clause 'or an object of class "difftime"' should be removed.

It would be nice if (Date + difftime) could use '+.Date'. But, I think it would
not be easy. One way is making a virtual class that includes "Date", "POSIXct",
and "difftime", say "DateTimeComp", so that the 'class' attribute of
"Date" is c("DateTimeComp", "Date");
"POSIXct" is c("DateTimeComp", "POSIXt", "POSIXct");
"POSIXlt" is c("DateTimeComp", "POSIXt", "POSIXlt");
"difftime" is c("DateTimeComp", "difftime").
Then, define '+.DateTimeComp' or 'Ops.DateTimeComp' that ensures that (Date +
difftime) uses '+.Date'. If it is chosen to define 'Ops.DateTimeComp', the
definition could be like this.